by Rachel Davies
Mathematics is one of those school subjects, (perhaps it is the primary one of such subjects), that is always going to prove difficult, challenging and even controversial.
The number of times that parents will have to sit with their children and wade through mathematical problems set for homework is always likely to be considerable.
It is also quite likely that many children will encounter problems with mathematics as they proceed through school. It is so consistently a subject that children either get or they don’t, and very often children struggle and become stressed out by the challenges that mathematics presents. This should set alarm bells ringing and make us want to do all that we can to alleviate this situation.
One way to potentially help alleviate and even remedy these problems with mathematics is to help children early on, in the early childhood years of education, to begin to cope with mathematics and all its concepts and ideas that can often seem abstract and obtuse to developing minds.
Pleasant and attractive names have been given to this process of introducing mathematics such as “My first steps in math” and “growing with mathematics”. But the aim is clear enough despite these cozy and friendly descriptors; what early childhood educators are trying to do is gently introduce mathematics and so lay foundations for the future learning.
These programs have been established in appreciation of cognitive and social theories about what can and even should be done in first and early mathematics learning. The viewpoint is taken that children must be seen as active learners who can and will construct their own understandings of mathematics through interaction with both their peers and the learning environments that they are exposed to.
Key areas for early mathematical learning have, therefore, been identified through research and analysis of how best little children learn and begin to conceive of and cope with mathematical knowledge. These key areas are: Numbers and operations, algebra, geometry, measurement and data analysis and probability.
For those that are not particularly strong mathematically these identified areas might sound too advanced and challenging but when they are broken down they look less daunting. For example, numbers and operations is a key focal point for early years’ mathematics. Little children are guided to learn to count accurately and with understanding of what they are doing. They begin to compare and put numbers in order through using concrete objects – counting them – and then moving on to symbols.
So for counting and numbers recognition little children will be counting and estimating the numbers of things that they can see or touch – whether concrete or pictorially. They will be comparing and ordering objects and beginning to recognize and write number symbols to represent their counting. They will be joining and breaking numbers up in the first steps of using numbers for calculation.
Algebra can be a tough part of mathematics but in early years learning children will benefit from beginning to develop algebraic thought through sorting and classifying objects and pictures; but also going on to identifying, describing, copying and creating patterns of actions, movements, sounds and objects.
Geometry is quite natural and a part of the early childhood years of experience. Little children are intuitively interested in the shape, size and general form of things and so geometric concepts and language can quite readily be incorporated into what they do as a part of their early years of education. Investigating the properties of solids and shapes and describing their attributes are those first geometric steps. Hearing and using the names given to those shapes is laying the foundations for future understanding of geometry.
Measurement too is a natural enough part of little children’s early learning experiences. Objects get looked at and described and slowly it is realized that they can be described in terms of length, weight, size and even capacity. This can be as simple as using words like long and short but will move on to ordering objects based on their measurable and measured characteristics. More abstract measurement may occur too, such as looking at a calendar and understanding the delineation and measurement of time.
Data analysis and probability seems like it would be among the most concept laden and so too most difficult areas to address, but again what we are talking about here are simple introductions to ideas. So, again we are looking at little children learning to classify things that they see – such as “is it the same or different?” they will be thinking about the attributes of things such as shape, size and color.
But they will also progress from these simple classifications to analysis, so that they can begin to look at simple graphs and begin to think of probabilities. For example, they may be looking at pictorial graphs of “Who Is Taller?” or “Who Has More?” and they may start to do graphing and so data analysis such as observing the weather and keeping a weather chart.
All of these things, when we look at them and break them down into their constituent parts and activities are really quite basic and straightforward and can be quite easily integrated into the lives of little children and so too their learning. But they are important learning activities and they are those early and tentative steps to developing mathematical awareness and so potential comfort and success with mathematics later on.
Any and all early learning centers that are worthy of that title should have a thorough understanding of these early and basics steps into the world of mathematics. They should be able to foster and nurture a general awareness and skills in observation, and so classification and analysis, that will help these early learners overcome the all too common pains and problems associated with learning and really understanding mathematics.
The writer is an education consultant in Sydney, Australia.